Infinite Right Triangles In A Semicircle

thingiverse

This geometry manipulative demonstrates a relationship between circles and right triangles: whenever you inscribe a triangle inside a circle where one side of the triangle is a diameter of the circle, then it will be a right triangle with the diameter of the circle as the hypotenuse. (There are other ways to state it.) This manipulative lets you move the free vertex along a semicircular arc and verify that the right-angle block remains oriented toward the fixed ends of the diameter, as well as to confirm that the two acute angles always sum to 90 as required in a right triangle.